Topology invisible to eigenvalues in obstructed atomic insulators

Abstract

We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all points in the Brillouin zone and, therefore, appear equivalent in a classification based on eigenvalues. We derive examples where such "irrep-equivalent" phases can be distinguished by a quantized Berry phase or generalization thereof. These examples constitute a generalization of the Su-Schrieffer-Heeger chain: neither phase is topological, in the sense that localized Wannier functions exist, yet there is a topological obstruction between them. We refer to two phases as "Berry obstructed atomic limits" if they have the same irreps, but differ by Berry phases. This is a distinct notion from eigenvalue obstructed atomic limits, which differ in their symmetry irreps at some point in the Brillouin zone. We compute exhaustive lists of elementary band representations that are irrep-equivalent, in all space groups, with and without time-reversal symmetry and spin-orbit coupling, and use group theory to derive a set of necessary conditions for irrep-equivalence. Finally, we conjecture, and in some cases prove, that irrep-equivalent elementary band representations that are not equivalent can be distinguished by a topological invariant.

18 pages, plus tables and Supplementary Material

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• Interacting topological quantum chemistry of Mott atomic limits
• Obstructed insulators and flat bands in topological phase-change materials
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Energy density as a probe of band representations in photonic crystals
• Pfaffian invariant identifies magnetic obstructed atomic insulators
• The destiny of obstructed atomic insulator under correlation
• Emergent chirality and enantiomeric selectivity in layered NbOX${}_2$ crystals
• Topological Dislocation Response in Elementary Semiconductors